Discontinuous Galerkin methods with plane waves for time-harmonic problems
- Institute of Sound and Vibration Research, University of Southampton, Southampton, SO17 1BJ (United Kingdom)
A general framework for discontinuous Galerkin methods in the frequency domain with numerical flux is presented. The main feature of the method is the use of plane waves instead of polynomials to approximate the solution in each element. The method is formulated for a general system of linear hyperbolic equations and is applied to problems of aeroacoustic propagation by solving the two-dimensional linearized Euler equations. It is found that the method requires only a small number of elements per wavelength to obtain accurate solutions and that it is more efficient than high-order DRP schemes. In addition, the conditioning of the method is found to be high but not critical in practice. It is shown that the Ultra-Weak Variational Formulation is in fact a subset of the present discontinuous Galerkin method. A special extension of the method is devised in order to deal with singular solutions generated by point sources like monopoles or dipoles. Aeroacoustic problems with non-uniform flows are also considered and results are presented for the sound radiated from a two-dimensional jet.
- OSTI ID:
- 20991614
- Journal Information:
- Journal of Computational Physics, Vol. 225, Issue 2; Other Information: DOI: 10.1016/j.jcp.2007.02.030; PII: S0021-9991(07)00096-4; Copyright (c) 2007 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9991
- Country of Publication:
- United States
- Language:
- English
Similar Records
A CLASS OF RECONSTRUCTED DISCONTINUOUS GALERKIN METHODS IN COMPUTATIONAL FLUID DYNAMICS
A Reconstructed Discontinuous Galerkin Method for the Compressible Navier-Stokes Equations on Hybrid Grids